pp {lmomco} | R Documentation

## Plotting-Position Formula

### Description

The plotting positions of a data vector (`x`) are returned in ascending order. The plotting-position formula is

pp_i = frac{i-a}{n+1-2a} mbox{,}

where pp_i is the nonexceedance probability F of the ith ascending data value. The parameter a specifies the plotting-position type, and n is the sample size (`length(x)`).

### Usage

    pp(x,a=0)

### Arguments

`x` | A vector of data values. The vector is used to get sample size through `length()`.
`a` | A value for the plotting-position formula. Default is `A=0`, which returns the Weibull plotting positions

### Value

An R `vector` is returned.

### Note

Various plotting positions have been suggested in the literature. Stedinger and others (1992, p. 18.25) comment that "all plotting positions give crude estimates of the unknown [non]exceedance probabilities associated with the largest (and smallest) events." The various plotting positions are summarized in the follow table.

hline Name | a | Motivation
hline Weibull | 0 | Unbiased exceedance probability for all distributions
Median | 0.3175 | Median exceedance probabilities for all distributions
APL | about 0.35 | Often used with probability-weighted moments
Blom | 0.375 | Nearly unbiased quantiles for normal distribution
Cunnane | 0.40 | Approximately quantile unbiased
Gringorten | 0.44 | Optimized for Gumbel distribution
Hazen | 0.50 | A traditional choice
hline |  |

### Author(s)

W.H. Asquith

### References

Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E., 1992, Frequency analysis of extreme events, in Handbook of Hydrology, chapter 18, editor-in-chief D. A. Maidment: McGraw-Hill, New York.

### See Also

`nonexceeds`, `pwm.pp`

### Examples

    Q <- rnorm(20)
    PP <- pp(Q)
    plot(PP,sort(Q))

    Q <- rweibull(30,1.4,scale=400)
    WEI <- parwei(lmom.ub(Q))
    PP <- pp(Q)
    plot(PP,sort(Q))
    lines(PP,quawei(PP,WEI))

[Package lmomco version 0.92 Index]